Combine chopped chocolate and cocoa powder in medium metal bowl. Add 1 3/4 cups boiling water and whisk until chocolate is melted and mixture is smooth. Set aside.

Sift flour, baking soda, and baking powder into another medium bowl.Using electric mixer, beat both sugars and mayonnaise in large bowl until well blended, 2 to 3 minutes. Add eggs 1 at a time, beating until well blended after each addition. Beat in vanilla. Add flour mixture in 4 additions alternately with the melted chocolate mixture in 3 additions, beating until blended after each addition and occasionally scraping down sides of bowl.